Question: Multiply and simplify the following complex numbers: $({3-3i}) \cdot ({-2+2i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3-3i}) \cdot ({-2+2i}) = $ $ ({3} \cdot {-2}) + ({3} \cdot {2i}) + ({-3i} \cdot {-2}) + ({-3i} \cdot {2i}) $ Then simplify the terms: $ (-6) + (6i) + (6i) + (-6i^2) $ Imaginary unit multiples can be grouped together. $ -6 + (6 + 6)i - 6 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -6 + (6 + 6)i - (-6) $ The result is simplified: $ (-6 + 6) + (12i) = 12i $